Related papers: Testing for separability is hard
We introduce a novel choice dataset, called joint choice, in which options and menus are multidimensional. In this general setting, we define a notion of choice separability, which requires that selections from some dimensions are never…
This paper develops a method to use singles' data in a non-parametric revealed preference setting of collective household choice. We use it to test the controversial assumption of preference stability between singles and couples, without…
It is common to assume in empirical research that observables and unobservables are additively separable, especially, when the former are endogenous. This is done because it is widely recognized that identification and estimation challenges…
We derive and study a significance test for determining if a panel of functional time series is separable. In the context of this paper, separability means that the covariance structure factors into the product of two functions, one…
Numerous papers ask how difficult it is to cluster data. We suggest that the more relevant and interesting question is how difficult it is to cluster data sets {\em that can be clustered well}. More generally, despite the ubiquity and the…
The problem of attempting to learn the mapping between data and labels is the crux of any machine learning task. It is, therefore, of interest to the machine learning community on practical as well as theoretical counts to consider the…
Human evaluation of generated language through pairwise preference judgments is pervasive. However, under common scenarios, such as when generations from a model pair are very similar, or when stochastic decoding results in large variations…
We investigate the problem of deciding whether a given preference profile is close to having a certain nice structure, as for instance single-peaked, single-caved, single-crossing, value-restricted, best-restricted, worst-restricted,…
Estimating the difficulty of a dataset typically involves comparing state-of-the-art models to humans; the bigger the performance gap, the harder the dataset is said to be. However, this comparison provides little understanding of how…
An experimenter seeks to learn a subject's preference relation. The experimenter produces pairs of alternatives. For each pair, the subject is asked to choose. We argue that, in general, large but finite data do not give close…
Analyzing the covariance structure of data is a fundamental task of statistics. While this task is simple for low-dimensional observations, it becomes challenging for more intricate objects, such as multivariate functions. Here, the…
Recent progress towards theoretical interpretability guarantees for AI has been made with classifiers that are based on interactive proof systems. A prover selects a certificate from the datapoint and sends it to a verifier who decides the…
Given well-shuffled data, can we determine whether the data items are statistically (in)dependent? Formally, we consider the problem of testing whether a set of exchangeable random variables are independent. We will show that this is…
We solve a well known, long-standing open problem in relational databases theory, showing that the conjunctive query determinacy problem (in its "unrestricted" version) is undecidable.
Given the stated preferences of several people over a number of proposals regarding public policy initiatives, some of those proposals might be judged to be more ``divisive'' than others. When designing online participatory platforms to…
In discriminating between objects from different classes, the more separable these classes are the less computationally expensive and complex a classifier can be used. One thus seeks a measure that can quickly capture this separability…
I survey recent progress on a classic and challenging problem in social choice: the fair division of indivisible items. I discuss how a computational perspective has provided interesting insights into and understanding of how to divide…
Although hypothesis tests play a prominent role in Science, their interpretation can be challenging. Three issues are (i) the difficulty in making an assertive decision based on the output of an hypothesis test, (ii) the logical…
The satisfiability problem for SPARQL patterns is undecidable in general, since the expressive power of SPARQL 1.0 is comparable with that of the relational algebra. The goal of this paper is to delineate the boundary of decidability of…
Prompted by an example related to the tensor algebra, we introduce and investigate a stronger version of the notion of separable functor that we call heavily separable. We test this notion on several functors traditionally connected to the…